Having self-awareness means being in control of your emotions, thoughts and actions. You do not respond to situations impulsively but reflectively. The Bible actually teaches Christians to be in control of their emotions, thoughts and actions.
Most conflicts take place when one or all parties involved fail to check themselves and just do or say something without thinking. As a follower of Christ, we are expected to know and examine the intents of our hearts in the sight of the Lord. Only He can determine whether something is wrong or not.
It is indeed rewarding to get acquainted with our own emotions and thoughts, but only God knows us better than we do. That is why we should seek the help of the Holy Spirit, to reveal things about ourselves, so we can do something about them.